- Allott & Uchida
- O&C claim that heuristics that involve information gain should be used. Allott & Uchida state that classical logic and O&C’s probabilistic account of conditionals and of inference must be supplemented by accounts of processing.
- Brighton and Olsson
- O&C discuss rational analysis as a process model used to develop optimal behavior. However, Brighton and Olsson believe that functional analysis can occur without a need for optimality.
- Danks & Eberhardt
- Danks & Eberhardt agree with O&C that the teleological explanations of human behavior are desirable, but they need a stronger foundation. They attest that Bayesian inference is neither a normative principle nor a subject of optimality as a result of people approximating explanations.
- Neys
- Neys shares that O&C’s modeling has an exclusive focus on output data which could lead to biased conclusions. He indicates that people are constantly trying to meet the norm.
- Evans
- O&C state that individuals resemble Bayesian reasoners more closely than standard logic. Evans agrees that the Bayesian model is better for real world reasoning than one based on truth-functional logic. However, Evans doesn’t know why O&C need to fit a normatively rational model to human reasoning.
- Griffiths
- Griffiths further examines the strengths and weaknesses of Bayesian models of cognition. Strengths include the systematicity of rational explanations, transparent assumptions and combining symbolic representation with statistics. Some of the challenges include providing psychological mechanisms, explaining origins of knowledge and describing how people make new discoveries.
- Hahn
- Hahn believes that an increase in explanatory power can be achieved by restricting a psychological theory. Although cognitive neuroscience experiments can lead to results, they are not as significant because of the successful opposite trend of O&C.
- Halford
- O&C believe that confidence is a function of informativeness. Halford counters that confidence is inversely related to complexity and that Bayesian rationality should be replaced by principles regarding cognitive complexity.
- Khalil
- Khalil examines the question of rationality and whether humans use classical deductive logic or probabilistic reasoning. He attests that organisms do process information and respond to the environment in ways that qualify them as rational.
- Liu
- Liu proposes that conditional probability hypothesis exists only when reasoners explicitly evaluate probability of conditionals, but that it may not exist when making (MP) inferences.
- McKenzie
- O&C suggest that deductive reasoning is parsimonious at a local and global level. They focus on environmental structure at the computational and algorithmic levels.
- Nelson
- Nelson believes that naive heuristic strategies can perform better than “optimal models.” Thus the normative role of the theoretical model and the adaptiveness of human behavior should be reexamined.
- Oberauer
- O&C state that people use probabilistic information to reason with unknown information. Oberauer believes that the probabilistic view on human reasoning has high a priori rationality and that that data by O&C is ambiguous.
- O’Brien
- O&C have rejected logic and supported probability theory. O’Brien explains that the mental-logic theory is based on logic that developed through bioevolutionary history to gain an advantage in making simple inferences.
- Over and Hadjichristidis
- O and H have an issue with O&C’s assumption that minor premises in conditional inferences are always certain, and believe that Jeffrey’s rule is not limited enough to account for actual probability judgements.
- Pfeifer and Kleiter
- They address O&C’s probabilistic approach from a probability logic standpoint. They discuss coherence, normativity, logic, and probability from this viewpoint.
- Poletiek
- Poletiek proposes an alternative falsification test to the logical falsification theory of testing. Conversely to logical falsification theory, the Severity of Test is an explanation that involves confirming evidence, instead of falsifying.
- Politzer and Bonnefon
- They agree with O&C that human reasoning cannot be purely based on logic. However, they have qualms with BR because it doesn’t address how conclusions are formed. Additionally, they believe that O&C ignore the importance of defining uncertainty.
- Schroyens
- They challenge the normativeness of BR by bringing up the fact that a rational analysis consists largely on individuals’ differing environments and goals as influences on their rationality. Furthermore, Schroyens believes that it is misleading when O&C ignore algorithmic-level specifications when comparing probabilistic and nonprobabilistic theories.
- Stenning and van Lambalgen
- They do not agree with O&C’s claim that logical methods cannot encompass nonmonotonicity, and therefore a probabilistic approach is required. They give examples of where BR fails to account for some forms of nonmonotonicity, and further suggest that a non-Bayesian theory must be used in addition.
- Straubinger, Cokely, Stevens
- While O&C solely address adult reasoning, S/C/S approach reasoning as something that varies over an individual’s lifespan. Because of the variations between individuals and age groups, S/C/S believe that one model (BR) isn’t sufficient to describe human reasoning as a whole.
- Wagenmakers
- Wagenmakers agrees that the information gain model is the best model to describe the Wason card task. However, he questions why participants don’t select all four cards given the information gain model. He also wonders if incentive, like money, would change the results.
Author’s Response:
R2.1:
O&C denounce Evans’ Dual Process view because it seems possible that System 1 and System 2 could contradict one another. Additionally, they claim that addressing individual differences in reasoning isn’t necessary for determining whether there is a single or multiple human reasoning systems.
R2.2:
The authors observe that deductive reasoning, which is certain, is not observed outside mathematics and thus, their account of reasoning, involves making pragmatic choices due to uncertainty. Thus, rather than working from the “premises alone”, BR allows for “uncertain, knowledge rich” inference.
R2.3:
O&C counter Politzer & Bonnefon’s criticism by providing examples (algorithms and constraint satisfaction neural network implementation of the probabilistic approach) of how BR accounts for the generation of conclusions.
R3.1:
O&C respond to Pfeifer & Kleiter’s statement, that the probability theory inherently includes classic logic, by saying a Bayesian inductive perspective is necessary because classic logic isn’t very applicable to everyday life.
R3.2:
O&C claim that adding a condition of relevance doesn’t address the uncertainty problems because elements outside of mathematics are inherently uncertain. Furthermore, O’Brien’s system doesn’t correctly capture the intuitions of relevance between antecedent and consequence.
R3.3:
The authors argue that resolving clashes between premises can only be obtained by differentiating between stronger and weaker arguments, and degrees of confidence in the premises of those arguments.
They posit that logical methods provide no natural methods for expressing such matters of degree; but dealing with degrees of belief and strength of evidence is the primary business of probability theory.
R3.4:
O&C respond to objections regarding the generalization of probabilistic reasoning and existing conflicts between prior beliefs and logical reasoning. They posit that the “description of behavior in logical or probabilistic terms doesn’t mean that the behavior is governed by logical and probabilistic processes”. The conclude that without probabilistic reasoning, logic cannot accurately capture human patterns of thought
R3.5:
O&C justify the Bayesian approach as a “pragmatic” choice given its wide application in the cognitive and brain sciences. They also assert that the Bayesian assumptions may be “too weak” insofar as it imposes “minimal coherence criteria” on beliefs. Lastly, they dismiss objections regarding justification as they propose probability as a “better” (not the best) means of dealing with uncertainty.
R3.6:
O&C respond to concerns regarding the “rigidity” and “uncertainty” of Bayesian probability. First, they assert that BR doesn’t need to account for all uncertainty, regarding conditionals, as some uncertainty isn’t relevant to the data. Second, they explain that the apparent lack of “rigidity” is Bayesian as it accounts for “pragmatic utterances”. Lastly, they disagree that people can reason deductively about probability intervals as new information is always incorporated from world knowledge.
R3.7:
The authors posit “disinterested” and “goal oriented” methods of inquiry. The former aims to maximize the expected amount of information gotten from a task while the latter maximizes the expected utility of getting information. By adopting a “goal oriented” method, they avoid the postulation of “specific machinery”.
R4: (comprehensive)
The authors criticize “algorithmic” models (eg connectionist models) insofar as they shed no light regarding “why” the modeled processes function. They also argue that “ecological rationality” supplements normative rationality and “rational analysis aims to explain ecological rationality”. Moreover, they posit that rational analysis is “goal specific” insofar as “rational” refers to information processing systems.
They also acknowledge the challenges faced when attempting to implement BR on an algorithmic level. Notwithstanding, they assert that “understanding the rational solution to problems faced by the cognitive system crucially assists with explanation in terms of representations and algorithms”. Thus, rational analysis assists algorithmic explanation.
Also, O&C acknowledge that rational analysis may be challenged when there are many, near optimal, rational solutions and, sometimes, finding exactly the optimal solution may be over-restrictive. In such cases, they suggest rational analysis will select a solution based on its “relative goodness”. They also justify the simplicity of the naive Bayes model as it can be justified by Bayesian reasoning.
R5:
First, the authors reveal a doxastic and factual distinction insofar as changing degrees of belief doesn’t entail a change in the real conditional probability. Also, the authors respond to objections regarding the BR model. Most importantly, they state that the experiments were performed “pragmatically” insofar as “it conforms to the current demand of most journals”.
Discussion Questions:
- Many commentators feel that BR doesn’t provide an adequate explanation for how people generate conclusions. Could fast and frugal heuristics serve as an explanation? In other words, to what extent do fast and frugal heuristics serve as the “specific machinery” for probabilistic reasoning?
- Is BR normative or descriptive? Are there any tensions between rational analysis and ecological rationality insofar as the former seems normative and the latter accounts for individual differences.
- Why is it that people seem more rational in the real world than in the laboratory? That is, why are there more violations of logic when in a controlled setting?
I’m interested in (and perhaps just confused about) Politzer and Bonnefon’s response to O&C that, while the probabilistic model is all well and good, it does not provide an explanation for how we come to conclusions. P&B state that probabilism is only suited for evaluating conclusions, not creating them (100). They concede that probabilism is a useful model, but that mixed model that includes uncertainty and deduction is the best-suited model (100). Perhaps this is bringing skepticism into the conversation where it does not need to be, but do we not arrive at all logical conclusions by way of a probabilistic process? Logical conclusions may be “airtight” given that the premises are true, but can we ever say that premises are 100% true? I see the internal monologue that gives rise to conclusions as: “Based on the evidence available to me at the moment, it is most likely that X and Y are true. If X and Y are true, then Z.” I would consider this to be using the probabilistic model to arrive at a conclusion, but perhaps some see this as an example of a mixed model.
I believe this is what O&C are getting at in their response to P&B when they say that “logic and probability are theories of the nature of inferential relationships between propositions” (107). In their response, I’m confused by O&C’s statement that “from [logical and probabilistic] perspectives, any set of information potentially generates an infinite set of possible conclusions” (107). Given the rules of rationality, any set of information should generate only one probable, rational conclusion. Are all of the other possibilities then still logical but not rational?
Similar to Carly and Tim’s question on the role of fast and frugal heuristics in probabilistic reasoning, I also wonder about the usage of heuristics in the probabilistic models discuss. Through the PHM, Oaksford and Charter explain the different types of heuristics, such as standard logical quantifiers versus generalized quantifiers (82). O&C claim that heuristics that are sensitive to information gain must be involved, yet the information has to be important to the reasoned and not simply sought (85). This makes me wonder about the role of intuitive heuristics as explained by Neys.
Neys claims that people typically select responses that are cued by intuitive heuristics and that people are constantly trying to meet the norm (88). Neys describes that problems in which intuitive beliefs conflict with the logical response take longer to respond to and are inspected more carefully (compared to problems in which beliefs and logic agree) (88). This makes me wonder about the relationship between intuitive heuristics and learned logic. Can intuition learn to become logical? And does that transform intuition to a conscious process as oppose to a spontaneous process? Can we say that they are two different types of heuristics? Or is one bond to transform into the other?
I’m slightly confused by Evans’ critique of Bayesian rationality (88–89).
Evans complains that Oaksford and Chater fail to offer a descriptive account of human reasoning: “I want to know what people are actually doing and how” (89).
Bayesian rationality successfully explains apparently irrational behavior. Most people are guilty of the confirmation bias (and fail to make the falsifying response) when given the Wason selection task, for example. The logicist would deem this behavior irrational. Bayesian rationality, however, suggests that the confirmation bias actually helps to maximize information gain and is thus consistent with rational decision-making. Bayesian rationality allows us to say much of the same for people’s conditional inference rates. People endorse the inference patterns they do because they—rationally—take into account the probability of the conclusion given the minor premise.
Evans suggests that these explanations of apparently irrational behavior, though compelling, constitute a normative, not descriptive, account of behavior. But how is that so? Isn’t Bayesian rationality surveying what we actually do and offering explanations of our behavior? (Doesn’t this exactly satisfy Evans’ request?) It seems to me that Bayesian rationality is quite descriptive. Maybe these descriptive norms can be included in a normative account? Perhaps there is no need to distinguish normative norms from descriptive ones. (Is that possible?)
The question raised by Carly, Timmy, and Nosagie on whether Bayesian rationality is normative or descriptive is an interesting one and I am particularly drawn to Evans commentary. Oaksford and Chater denounce Evans’ Dual Process view and would argue that Bayesian Rationality is normative. Furthermore, O&C reject any form of rationality that cannot be justified by a normative system. However, I entertain the Dual Process view and think O&C’s reason for dismissing it is rather problematic. O&C conceive the possibility that System 1 and System 2 of the Dual Process view contradict each other. Is this contradiction enough to reject the Dual Process view? Is rationality possible if it is not justified by a normative system?
As a cognitive psychologist, Evans claims that he wants to know what people are actually doing and how. Therefore, he is unsatisfied with O&C’s use of exercises such as the Wason selection task that simply show there is some normative account of behavior (89). I find the idea that people follow normative rules (Rationality 2) but also can “often achieve everyday goals by implicit processes such as associative learning” (Rationality 1) much more appealing (89). I image that there are many people in the same boat and this raises the interesting question about how we study rationality. It seems rather simplistic to study rationality by “observ[ing] some behavior, assum[ing] that it is rational, [and] find[ing] a normative theory that deems it to be so” (89). Is it possible to study rationality without a normative system?
Evans claims that O&C overstate everyday rationality in the original book. O&C ask, “Why do the cognitive processes underlying everyday rationality consistently work?” (30). Evans claims they don’t and points to several examples from psychological literature (e.g. outcome bias, hindsight bias, overconfidence, and planning fallacy) (89). How does everyday rationality and its underlying cognitive processes differ from being a generally rational person?
Since Nosagie wasn’t too happy about my long post last time, I’ll try to keep it short and sweet for him this time. I, like Devon, am somewhat appeased by the notion that BR is not as rigid as the critics (and we) thought it to be. They give us a clear example of revising the probabilities and accounting for real world uncertainty: “suppose I believe ‘if the key is turned, the car starts’; and I am told: ‘the car didn’t start this morning.’ This would be a pragmatically pointless remark, if the key had not been turned. I therefore infer that the key was turned, and the car didn’t start for some other reason. Thus, I revise down the probability of the relevant conditional dramatically’” (109). They argue that in cases like these and the sunny day/park example (108) that logic does not differentiate between stronger and weaker arguments based on a variety of premises. They do however concede that in a world like math where all conditionals are false, logic has just as much merit as BR. Before I give up on logic, it seems that there must be some other realm where logic could hold some merit. Does this realm exist? And even if this is the case, why not just go full BR if they are as I propose, equal in merit?
In class we discussed the usefulness of BR, and some people were against it because of its drawbacks. For example, the only way to interpret any new information would depend on the information that we already had. O&C try to challenge this perspective by arguing that the “rigidity” and “uncertainty” this causes is actually not present when this system of rationality is used. O&C believe that BR only accounts for “pragmatic utterances,” but I am still not convinced that BR is more useful because of this. If my primary belief is subjective and I believe that it is important in the following interpretation of my probability calculus, anything can be applied. Because BR allows many things to be the cause of any belief or occurrence, it is not a useful system. If we are seeking what causes something and are still using information that proves our conclusion to be untrue, we do not have evidence for our conclusion.
On another note, Devon mentioned that rationality may be linked to education, culture, or class. Like Devon, I also agree with the perspective that O&C have taken on this concept. They argue that rationality is actually connected to societal constructs and discourses, whereas “logical competence is learned.” This may be the reason why rational is more present in the real world than in the laboratory. There can be violations of logic because there are specific instances in which is learned, whereas rationality is formed from a combination of things and lacks the rules that are present in logic.
With this in mind, I ask, how do we define “pragmatic” and what exactly is relevant in BR? What distinguishes how we obtain rationality and how we obtain “logical competence?
In class, we talked about Bayesian Rationality and logicist conception of rationality mostly as if they were a binary. A few people expressed that they believed the two could coexist somehow but we did not discuss it in depth. O&C describe how the two relate by saying, “The Bayesian inductive perspective is required not because classic logic is incorrect, but because outside mathematics, it rarely, if ever applies” (107). Furthermore they describe BR as, “a generalization of logic, allowing degrees of uncertainty” (108). Therefore, O&C argue that BR includes logic but expands upon it to accommodate reasoning that occurs in the real world in response to uncertainty. I found this whole section very helpful after our Thursday discussions and feel much more open to Bayesian Rationality.
Since we have started talking about rationality, however, I have kept wondering to what degree rationality (and individual differences in rationality) is linked to education, culture, or class. After reading this article, I now believe that it is not necessarily rationality that is linked to these characteristics, but logic. O&C argue, “Logical reasoning is a late and cognitively challenging cultural innovation, rather than a core component of our mental machinery” (106) I think we can all sympathize with this statement, illustrated by how many of us failed the Watson Selection Task on our first day of class. This connects directly to O&C’s idea that, “logical competence is learned, either directly or indirectly” (114) and therefore they argue that logic should not be at the center of a model of human rationality. I would tend to agree with this argument, because if logic was given such a heavy weight it seems like someone with a higher level of education or more logical reasoning experience would automatically be more rational than someone else. I believe this could be very problematic and I want to hear other people’s thoughts.
How do we disentangle logic and rationality? How much of a role do people think logic plays in rationality and what effect does this have on whether rationality is linked to education, culture, and class? Furthermore, is mathematics really the only way to find a situation that requires only logical reasoning? Is it fair of O&C to say we do not use logic when we reasoning in “real world” situations?